Open AccessJournal Article
Numerical study on incomplete orthogonal factorization preconditioners
TLDR
In this article, incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations are presented.Abstract:
We design, analyse and test a class of incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations. Comprehensive accounts about how the preconditioners are coded, what storage is required and how the computation is executed for a given accuracy are presented. A number of numerical experiments show that these preconditioners are competitive with standard incomplete triangular factorization preconditioners when they are applied to accelerate Krylov subspace iteration methods such as GMRES and BiCGSTAB.read more
Citations
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A Bibliography of Publications of Iain S. Du
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Modified incomplete orthogonal factorization methods using Givens rotations
Zhong-Zhi Bai,Jun-Feng Yin +1 more
TL;DR: These modified incomplete Givens orthogonalization (MIGO) methods can preserve certain useful properties of the original matrix, and numerical results are used to verify the stability, the accuracy, and the efficiency of the MIGO methods employed to precondition the Krylov subspace iteration methods such as GMRES.
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A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides
TL;DR: An adaptive simpler block GMRES algorithm for large linear systems with multiple right-hand sides is proposed and theoretical analysis is made to show the reason why the new algorithm is superior to its original counterpart.
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An optimized discrete grey multi-variable convolution model and its applications
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References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Journal ArticleDOI
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
Journal ArticleDOI
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.